caa a22 4500 465764576 CHVBK 20180323111910.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF01129595 doi (NATIONALLICENCE)springer-10.1007/BF01129595 Ruggeri T. Dipartimento di Matematica, Università di Bologna, Via Saragozza 8, 40123, Bologna, Italy aut Convexity and symmetrization in relativistic theories [Elektronische Daten] Privileged time-like congruence and entropy [T. Ruggeri] There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it — $$\bar h$$ — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruence $$\bar \xi _\alpha $$ . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas. Springer-Verlag, 1990 Continuum Mechanics and Thermodynamics Springer-Verlag 2/3(1990-09-01), 163-177 0935-1175 2:3<163 1990 2 161 https://doi.org/10.1007/BF01129595 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01129595 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ruggeri T. Dipartimento di Matematica, Università di Bologna, Via Saragozza 8, 40123, Bologna, Italy aut NATIONALLICENCE 773 0- Continuum Mechanics and Thermodynamics Springer-Verlag 2/3(1990-09-01), 163-177 0935-1175 2:3<163 1990 2 161 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer